Über die Zufuhr von Turbulenzenergie durch Grenzflächenreibung und labile Schichtung

Zusammenfassung In einer turbulenten Strömung wird die Arbeitsleistung der mittleren Schubspannung an den Begrenzungen durch deren Rauhigkeit in Turbulenzenergie umgewandelt. Das Resultat ist ein Austauschstrom dieser Energie von der Begrenzung in die Flüssigkeit hinein. Dies kann ein sehr wesentlicher Beitrag zur Aufrechterhaltung seiner Turbulenz werden, insbesondere in Fällen stabiler Schichtung in Bodennähe.In den bekannten Ableitungen des Richardsonschen Turbulenzkriteriums und in der gebräuchlichen Gleichung für die Änderung der Turbulenzenergie scheint man diesen Randeinfluß nicht zu berücksichtigen. Beide Beziehungen versagen außerdem bei Anwendung auf neutrale Schichtung. Für diesen Fall liefern sie, wie von K. L. Calder [1949] und O. G. Sutton [1949] bemerkt, eine ständige Zunahme der Turbulenzenergie, weil die Arbeitsleistungen der Zusatzgeschwindigkeiten gegen die turbulenten Schwankungen des Druckgradienten unberücksichtigt blieben. Bei einer korrekten Ableitung und Anwendung sind sie ebenso in Rechnung zu stellen wie die Konvergenz obigen Austauschstromes der Turbulenzenergie.

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On the supply of turbulent energy by boundary friction and unstable stratification

Summary In a turbulent current, the work of the average shearing stress is transformed into eddy energy by the roughness of its boundaries. The result is a turbulent transport of this energy from the boundary into the fluid. This may become an essential contribution to maintaining the turbulence of the current, especially in cases of stable stratification next to the bottom.This influence of the boundary has apparently been considered neither in the known derivations of Richardson's criterion of turbulence nor in the usual equation of the change of eddy energy which both, in addition, fail when being applied to neutral stratification. In this case, the criterion gives a permanent increase of eddy energy contrary to the observations already stated by K. L. Calder [1949] and O. G. Sutton [1949], since the work of the eddy velocities against the fluctuations of the gradient of pressure is not taken into account. In a correct derivation and application we have to consider both, this work and the convergence of the eddy flow of turbulent energy normal to the smoothed boundaries.

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Sur la formation d'énergie turbulente causée par la friction des surfaces de séparation et par la stratification labile

Résumé Dans un courant turbulent le rendement moyen du frottement tangentiel auprès des limites solides est transformé en énergie turbulente grâce à la rugosité de ces limites. Le résultat en est un transport de cette énergie à partir des limites solides jusqu'à l'intérieur de la fluide. Cette énergie peut essentiellement contribuer à la conservation de la turbulence du courant, surtout en présence d'une stratification stable au voisinage du sol.Il semble que l'on ne tienne pas compte de cet effet des limites solides dans les dérivations connues du critérium de turbulence d'après Richardson et dans l'équation usuelle concernant le changement de l'énergie turbulente. En outre, ces deux relations ne correspondent pas aux observations lorsqu'on essaie de les appliquer à la stratification neutre, ce qui était déjà constaté par K. L. Calder [1949] et par O. G. Sutton [1949]. Le critérium fournit dans ce cas-là une augmentation permanente de l'énergie turbulente parce que le rendement de la vitesse additionnelle qui a une influence affaiblissante sur les variations turbulentes du gradient de pression n'est pas considéré. Afin d'assurer une dérivation et une application correcte il est nécessaire de considérer l'influence affaiblissante de la vitesse additionnelle sur les variations du gradient de pression aussi bien que de tenir compte du transport de l'énergie turbulente à partir des limites solides jusqu'à l'intérieur de la fluide.

     

Constraints on the thermal evolution of continental lithosphere from U-Pb accessory mineral thermochronometry of lower crustal xenoliths,southern Africa

U-Pb isotopic thermochronometry of rutile, apatite and titanite from kimberlite-borne lower crustal granulite xenoliths has been used to constrain the thermal evolution of Archean cratonic and Proterozoic off-craton continental lithosphere beneath southern Africa. The relatively low closure temperature of the U-Pb rutile thermochronometer (~400-450 °C) allows its use as a particularly sensitive recorder of the establishment of "cratonic" lithospheric geotherms, as well as subsequent thermal perturbations to the lithosphere. Contrasting lower crustal thermal histories are revealed between intracratonic and craton margin regions. Discordant Proterozoic (1.8 to 1.0 Ga) rutile ages in Archean (2.9 to 2.7 Ga) granulites from within the craton are indicative of isotopic resetting by marginal orogenic thermal perturbations influencing the deep crust of the cratonic nucleus. In Proterozoic (1.1 to 1.0 Ga) granulite xenoliths from the craton-bounding orogenic belts, rutiles define discordia arrays with Neoproterozoic (0.8 to 0.6 Ga) upper intercepts and lower intercepts equivalent to Mesozoic exhumation upon kimberlite entrainment. In combination with coexisting titanite and apatite dates, these results are interpreted as a record of postorogenic cooling at an integrated rate of approximately 1 °C/Ma, and subsequent variable Pb loss in the apatite and rutile systems during a Mesozoic thermal perturbation to the deep lithosphere. Closure of the rutile thermochronometer signals temperatures of 𙠂 °C in the lower crust during attainment of cratonic lithospheric conductive geotherms, and such closure in the examined portions of the "off-craton" Proterozoic domains of southern Africa indicates that their lithospheric thermal profiles were essentially cratonic from the Neoproterozoic through to the Late Jurassic. These results suggest similar lithospheric thickness and potential for diamond stability beneath both Proterozoic and Archean domains of southern Africa. Subsequent partial resetting of U-Pb rutile and apatite systematics in the cratonic margin lower crust records a transient Mesozoic thermal modification of the lithosphere, and modeling of the diffusive Pb loss from lower crustal rutile constrains the temperature and duration of Mesozoic heating to 𙡦 °C for ₞ ka. This result indicates that the thermal perturbation is not simply a kimberlite-related magmatic phenomenon, but is rather a more protracted manifestation of lithospheric heating, likely related to mantle upwelling and rifting of Gondwana during the Late Jurassic to Cretaceous. The manifestation of this thermal pulse in the lower crust is spatially and temporally correlated with anomalously elevated and/or kinked Cretaceous mantle paleogeotherms, and evidence for metasomatic modification in cratonic mantle peridotite suites. It is argued that most of the geographic differences in lithospheric thermal structure inferred from mantle xenolith thermobarometry are likewise due to the heterogeneous propagation of this broad upper mantle thermal anomaly. The differential manifestation of heating between cratonic margin and cratonic interior indicates the importance of advective heat transport along pre-existing lithosphere-scale discontinuities. Within this model, kimberlite magmatism was a similarly complex, space- and time-dependent response to Late Mesozoic lithospheric thermal perturbation.     

Determination of Total Organic Carbon Content and δ13C in Carbonate-Rich Detrital Sediments

The determination of total organic carbon content and composition in detrital sediments requires careful removal of their carbonate minerals. In detrital sediments containing large amounts of carbonates, including dolomite, this can only be achieved by liquid acid leaching that may solubilise a significant proportion of the organic carbon. For a set of detrital sediments from the Himalayan system and the Amazon River as well as five geological reference materials, we determined the proportion of organic carbon (C_org) solubilised during acid leaching. This proportion is significant for all analysed sediments and generally tends to increase with the organic carbon content. Compared to other types of sediments analysed, clay fractions extracted from river sediments and bed sediments with very low organic carbon content have high and low proportions of acid soluble C_org respectively. In Himalayan and Amazon river sediments, the proportion of C_org solubilised during acid leaching was relatively constant with average values of 14 and 19 % respectively. Thus, it is possible to correct the C_org content for the dissolved organic carbon content measured after decarbonation. Data presented here show that C_org dissolved during liquid acid leaching must be taken into account. After careful calibration, the method presented here should, therefore, be applied to any carbonate-rich detrital sediment.     

Mid-Holocene to present-day evolution of the Indian monsoon in transient global simulations

The low-frequency evolution of Indian rainfall mean-state and associated interannual-to-decadal variability is discussed for the last 6000 years from a multi-configuration ensemble of fully coupled global transient simulations. This period is marked by a shift of Indian Summer Monsoon Rainfall (ISMR) distribution towards drier conditions, including extremes, and a contraction of the rainy season. The drying is larger in simulations with higher horizontal resolution of the atmosphere and revised land surface hydrology. Vegetation–climate interactions and the way runoff is routed to ocean modulate the timing of the monsoon onset but have negligible effects on the evolution of seasonal rainfall amounts in our modeling framework in which carbon cycling is always active. This drying trend is accompanied by changes in ISMR interannual-to-decadal variability decreasing over north and south India but increasing over central India (20°–25° N). The ISMR interannual-to-decadal variability is decomposed into six physically consistent regimes using a clustering technique to further characterize its changes and associated teleconnections. From 6 to 3.8 kyr bp, the century-to-century modulations in the frequency of occurrence associated to the regimes are asynchronous between the simulations. Orbitally-driven trends can only be detected for two regimes over the whole 6–0 kyr bp period. These two regimes reflect increased influence of ENSO on both ISMR and Indian Ocean Dipole as the inter-hemispheric energy gradient weakens. Severe long-term droughts are also shown to be a combination of long-term drying and internally generated low-frequency modulations of the interannual-to-decadal variability.

     

Vertical migration ofcentropages typicus (copepoda) in Chesapeake Bay,with some thoughts on migration studies

Centropages typicus was collected at two hour intervals over a diel cycle at a station near the Chesapeake Bay mouth. The species migrated upward at dusk and downward at dawn. Neither light, temperature, salinity, nor density appeared to cue the migration. Attention is drawn to the need for information on the extent and regularity of migration by individual organisms, and how the lack of such information may lead to poor interpretations of migration data.     

Die Vertikaländerung des beschleunigungsfreien Windes in äquatorialen Breiten

Zusammenfassung Wie in mittleren und höheren Breiten bedingt auch am Äquator die meridionale Temperaturverteilung eine Vertikaländerung des reibungs- und beschleunigungsfreien Windes. Allerdings darf man dabei keine Drehung des Windvektors erwarten, da, wie gezeigt wird, sowohl am Äquator als auch in seiner Umgebung ausschliesslich rein zonale stationäre und beschleunigungsfreie Strömungen (bei verschwindenden zonalen Änderungen des Temperatur- und Druckgradienten) in Betracht kommen.

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Summary At the equator vertical variations of a frictionless and unaccelerated wind are caused by the meridional distribution of temperature in a similar way as in higher latitudes. Nevertheless there cannot be expected any deviation of the wind vector with high since only pure zonal winds free of acceleration may be possible around the equator and in its neighbourhood.

     

Modellrechnungen zu winderzeugten Bewegungen in einem Meer mit Sprungschicht

Zusammenfassung Nach Erörterung der benutzten vertikal integrierten Bewegungsgleichungen für ein Meer mit Sprungschicht sowie der Ansätze für Schubspannung und Reibung werden die Beziehungen zwischen Spiegel- und Sprungflächenlage und die Wirkung des Windschubs auf einen geschichteten Kanal diskutiert. Es folgt die Beschreibung der Windschubwirkung auf tropische Modellmeere mit Sprungschicht. Insbesondere wird das Ergebnis einer den Verhältnissen im Arabischen Meer bei beginnendem Sommermonsun nahekommenden Modellrechnung beschrieben, in der sich die Sprungschicht vor der afrikanisch-arabischen Küste um mehrere Dekameter hebt (upwelling), vor der indischen Küste ebenso stark absenkt. Parallel diesen Küsten treten zwischen dem 8. und 16. Tag Wellenkämme und-täler in der Sprungschicht und in der Oberfläche in genau gleicher Art auf, wie sie A. Defant [1950/1951] aus Beobachtungen vor der kalifornischen Küste im Zusammenhang mit auf- und ablandigem Windschub abgeleitet hat. Wir zeigen noch, daß diese Wellen nichts mit fortschreitenden zu tun haben können und leiten die dafür gebräuchliche Formel für die Fortpflanzungsgeschwindigkeit aus den vertikal integrierten Bewegungsgleichungen ab.Abschließend wird das Modell einer idealisierten Nordsee mit sommerlicher Sprungschicht beschrieben, in dem das Massen- und Geschwindigkeitsfeld durch ein vorüberziehendes Tiefdruckgebiet Änderungen erfährt. Dem Luftdruckminimum folgt eine Mulde mit zyklonaler Wasserzirkulation in der Oberschicht nach, welche noch geraume Zeit nach Abzug des Tiefs anhält. Die Sprungschicht hebt sich südlich der Bahn des Tiefs um einige Meter und entfaltet eine kräftige, südwärts fortschreitende Wellenbewegung an der östlichen Begrenzung. Auch in der Unterschicht herrscht eine zyklonale Wasserzirkulation vor; das untere Wirbelzentrum bleibt aber hinter dem der Oberschicht zurück und holt es erst nach Abzug der Zyklone ein. Beide Wirbelzentren liegen dann unter einer sich abschwächenden Mulde in der Wasseroberfläche.Unsere Modelle zeigen, daß es mit den heutigen Hilfsmitteln im Prinzip möglich ist, nicht nur die Einflüsse aktueller meteorologischer Faktoren auf die Wasseroberfläche, sondern auch ihre Wirkung auf die Massenverteilung innerhalb des Meeres zu ermitteln. Zur modellmäßigen Darstellung der allgemeinen Zirkulation des Meeres sind allerdings die hier nicht berücksichtigten Vermischungsvorgänge in Rechnung zu stellen.

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Numerical models on wind produced motions in a sea with a pycnocline

Summary After a treatment of the system of vertically integrated equations of motion concerning a sea with a pycnocline we discuss the stress and friction terms used here and the general relations connecting the variation of the surface with that of the pycnocline as well as the effect of wind stress in a double-layered canal. After that we regard the effects of wind stress and pressure of air on tropical model oceans with a pycnocline. Especially the result of a numerical computation of the behaviour of an idealized Arabian Sea in the beginning of the summer monsoon is described: The pycnocline is lifting by several decameters in front of the African and Arabian shores (upwelling) and is descending by the same number of decameters in front of the Indian coast. Between the eighth and sixteenth day there are contrary wave crests and troughs in the surface and in the pycnocline parallel to the African and Indian shores of exactly the same kind as those already derived from observations in front of the Californian coast by A. Defant [1950/1951] in connection with on-shore an off-shore winds.Concluding, we describe the model of an idealized North Sea with a summer thermocline where the fields of mass and velocity are affected by a passing low. Its centre is followed by a trough in the surface and a cyclonic circulation in the upper layer continuing even a long time after the low had passed. In the south of its path the thermocline ascents some meters and at the eastern shore it develops a vigorous wave motion propagating southward. A cyclonic circulation prevails also in the layer beneath the thermocline; its centre lags behind the curl centre of the upper layer but at last joins it after the low left the model sea. Both curl centres then come to lie underneath the gradually diminishing trough in the sea surface.As shown by our models, the modern aids make it possible, not only to compute the effects of the actual meteorological events on the sea surface but also their effects on the mass distribution within the sea. If, however, a model of the general circulation in the oceans is to be given, there should, at any rate, be taken into account the mixing processes of water masses neglected here.

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Modèles numériques pour le calcul des mouvements dûs au vent dans une mer ayant une couche de densité à discontinuité

Résumé Pour une mer ayant une couche de densité à discontinuité on discute le système des équations de mouvements, intégrées verticalement et on expose les termes du frottement tangentiel dû au vent et ceux de la friction interne employés dans ce travail. Puis on traite les relations générales qui existent entre les variations de la surface et celles de la couche de discontinuité et on décrit les effets du frottement tangentiel dû au vent dans un canal à deux couches. Aprés cela on étudie l'effet du frottement tangentiel dû au vent et la pression atmosphérique exercée sur des modèles de mers tropiques ayant des couches de discontinuité. On décrit surtout le résultat du calcul numérique du comportement d'une mer idéalisée arabique au commencement de la mousson estivale. Suivant ce calcul, la couche de discontinuité s'élève par plusieurs décamètres (upwelling) devant la côte afro-arabique et elle s'abaisse en même degré devant la côte indienne. Entre le 8^ième et le 16^ième jour il se présente, parallèlement à ces côtes, des crêtes et des creux de vagues opposées dans la couche de discontinuité et dans celle de la surface. Ces vagues sont de la même espèce que celles que A. Defant [1950/1951] a déjà dérivées des observations faites devant la côte de la Californie en présence du frottement tangentiel dû aux vents de terre et de mer. On montrera que ces vagues ne peuvent avoir aucun rapport aux vagues progressives et nous dérivons des équations verticalement intégrées de mouvement la formule en usage pour la vitesse de propagation.Ênfin, on décrit le modèle de la mer idéalisée du Nord, dans laquelle on suppose une couche estivale de discontinuité. Dans ce modèle le champ de masse et le champ de vitesse subissent de changements par le passage d'une aire de basse pression, dont le minimum atmosphérique est suivi d'une dépression qui de sa part, dans la couche supérieure de l'eau, est accompagnée d'une circulation cyclonique, qui se maintient même quelque temps après le passage de l'aire de basse pression. Au sud de sa trajectoire la couche de discontinuité s'élève par plusieurs mètres; à sa limite orientale elle développe de fortes vagues qui se propagagent vers le sud. Dans la couche qui se trouve au-dessous de la couche de discontinuité, une circulation cyclonique est également prédominante; son centre est en retard sur celui de la couche supérieure qu'il ne rattrapera qu'après le passage du cyclone. Les deux centres cycloniques se trouvent alors au-dessous de la dépression en voie de s'exténuer à la surface de l'eau.Les modèles montrent que les ressources modernes permettent, en principe, de calculer non seulement les effets des facteurs météorologiques actuels à la surface de l'eau, mais aussi leurs effets sur la distribution des masses dans l'océan. Si l'on veut, cependant, représenter la circulation générale en mer au moyen d'un modèle, il est nécessaire de tenir compte des processus de mélange non considérés dans cette étude.

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Hierzu Tafel 7 mit Abb. 7a-e, Tafel 8 mit Abb. 11a-d, Tafel 9 mit Abb. 12a-e

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Herrn Professor A. Defant zum 81. Geburtstag gewidmet.     

Extraterrestrial chromite distribution across the mid-Ordovician Puxi River section, central China: Evidence for a global major spike in flux of L-chondritic matter

Previous studies of mid-Ordovician limestone in Sweden have shown that over a stratigraphic interval representing a few million years there is a two orders-of-magnitude enrichment in fossil L-chondritic meteorites (Ø = 1-21 cm) and sediment-dispersed extraterrestrial chromite (EC) grains (>63 μm). This has been interpreted as a dramatic increase in the flux of L-chondritic matter to Earth following the breakup of the L-chondrite parent body, which based on Ar-Ar gas retention ages (470 ± 6 Ma) of recently fallen meteorites occurred at about this time. Here we show that the general trend in the distribution of sediment-dispersed EC grains can be reproduced in the Puxi River section in central China. A total of 288 kg of limestone was searched for chrome spinels. In samples spanning the lower 8 m of the section, representing the Paroistodus originalis and Lenodus antivariabilis conodont zones, a total of 110 kg of limestone yielded only one EC grain. Similarly to the Swedish sections, EC grains begin to be common in the overlying L. variabilis Zone and remain common throughout the upper 9 m of the section, representing the L. variabilis, Yangtzeplacognathus crassus and L. pseudoplanus zones. In this part of the section 178 kg of limestone yielded 290 EC grains, with an average chemical composition very similar to chromite from recent L chondrites. In most of the beds over this interval one finds 1-4 EC grains per kilogram rock, a clear two orders-of-magnitude enrichment relative to the lower part of the section. Small bed-by-bed variations in the EC content over the upper interval most likely reflect small variations in sedimentation rates. The Puxi River section contains only very rare terrestrial chrome spinel grains, which can be distinguished already by their rounded, abraded appearance compared to the angular, pristine extraterrestrial spinels. In the mid-Ordovician, based on paleoplate reconstructions, the Puxi River site was positioned at mid-latitudes on the southern hemisphere a couple of thousand kilometers east of the Swedish sites. The prominent enrichment of EC grains over the same stratigraphic interval in China and Sweden is supporting evidence for a dramatic increase in the flux of L-chondritic matter to Earth shortly after the disruption of the L-chondrite parent body in the asteroid belt.     

On the interactions between planetary geostrophy and mesoscale eddies

Multiscale asymptotics are used to derive three systems of equations connecting the planetary geostrophic (PG) equations for gyre-scale flow to a quasigeostrophic (QG) equation set for mesoscale eddies. Pedlosky (1984), following similar analysis, found eddy buoyancy fluxes to have only a small effect on the large-scale flow; however, numerical simulations disagree. While the impact of eddies is relatively small in most regions, in keeping with Pedlosky’s result, eddies have a significant effect on the mean flow in the vicinity of strong, narrow currents.First, the multiple-scales analysis of Pedlosky is reviewed and amplified. Novel results of this analysis include new multiple-scales models connecting large-scale PG equations to sets of QG eddy equations. However, only introducing anisotropic scaling of the large-scale coordinates allows us to derive a model with strong two-way coupling between the QG eddies and the PG mean flow. This finding reconciles the analysis with simulations, viz. that strong two-way coupling is observed in the vicinity of anisotropic features of the mean flow like boundary currents and jets. The relevant coupling terms are shown to be eddy buoyancy fluxes. Using the Gent-McWilliams parameterization to approximate these fluxes allows solution of the PG equations with closed tracer fluxes in a closed domain, which is not possible without mesoscale eddy (or other small-scale) effects. The boundary layer width is comparable to an eddy mixing length when the typical eddy velocity is taken to be the long Rossby wave phase speed, which is the same result found by Fox-Kemper and Ferrari (2009) in a reduced gravity layer.